---
tags:
- kernel
- governance
- lambda
- gate
- provenance
- doi:10.5281/zenodo.19944926
library_name: kernels
license: apache-2.0
---

<p align="center">
  <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/tree/main/build/torch-universal/szl_lambda_gate"><img src="https://img.shields.io/badge/kernel%20hub-torch--universal-5b8dee?style=flat-square" alt="kernel hub"></a>
  <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/blob/main/MODEL_PROVENANCE.json"><img src="https://img.shields.io/badge/provenance-MODEL_PROVENANCE.json-3af4c8?style=flat-square" alt="provenance"></a>
  <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/blob/main/LICENSE"><img src="https://img.shields.io/badge/license-Apache--2.0-7e8aa3?style=flat-square" alt="license"></a>
</p>

# szl-lambda-gate

**Λ — a governance aggregator as a Hugging Face kernel.** A differentiable, torch.compile-friendly weighted-geometric-mean aggregator with an ADVISORY non-compensatory gate and runtime axiom self-checks, from [SZL Holdings](https://huggingface.co/SZLHOLDINGS).

> Companion to [`szl-governed-norm`](https://huggingface.co/SZLHOLDINGS/szl-governed-norm). Where that kernel makes a normalization *auditable*, this one makes a *governance decision* computable and checkable at the tensor layer.

## Interactive demo

> **Live demos (in-browser, nothing to install)** — [`lambda-gate-holo`](https://szlholdings-lambda-gate-holo.static.hf.space) (this kernel's holographic gate demo) · [`szl-kernels-live`](https://szlholdings-szl-kernels-live.static.hf.space) (unified suite demo).
>
> The quickstart above runs fully locally. For a full governed-kernel suite demo, see [szl-kernels](https://huggingface.co/SZLHOLDINGS/szl-kernels). For the live a11oy substrate, see [a11oy Space](https://huggingface.co/spaces/SZLHOLDINGS/a11oy).

## What Λ is — and is NOT (read this first)

Λ is the **weighted geometric mean** over axis scores in [0,1]:

\[ \Lambda(x) = \prod_i x_i^{w_i}, \quad \sum_i w_i = 1, \; w_i > 0, \; x_i \in [0,1] \]

It is a **non-compensatory, ADVISORY** roll-up: any single zeroed (or non-finite) axis drives the whole aggregate to 0 — a conservative "one bad axis fails the gate" signal. **Λ is NOT "proven trust" and NOT a closed theorem.** Its *uniqueness* (that the weighted geometric mean is the only aggregator satisfying the carried axioms) remains **Conjecture 1 — OPEN**. A gate "pass" is an advisory signal, never a guarantee. We label this honestly everywhere.

## Quickstart

```bash
pip install kernels torch
```

```python
import torch
from kernels import get_kernel

# Current `kernels` (>=0.15) requires an explicit revision/version + trust flag for org kernels:
lg = get_kernel("SZLHOLDINGS/szl-lambda-gate", revision="main", trust_remote_code=True)
# (once a tag is published you can pin it, e.g. revision="v0.2.0")

axes = torch.tensor([0.9, 0.8, 0.95])      # axis scores in [0,1]
score = lg.lambda_aggregate(axes)          # Λ(x) ∈ [0,1]
res   = lg.lambda_gate(axes, threshold=0.5)
print(res.score, res.passed, res.advisory) # advisory is always True

print(lg.selfcheck())                      # empirical A1–A4 checks + version
```

## API

| Function | Notes |
|---|---|
| `lambda_aggregate(axes, weights=None)` | Λ over the last dim. Differentiable, batched, torch.compile-friendly. |
| `lambda_gate(axes, weights=None, threshold=0.5)` | Advisory gate → `LambdaGateResult(score, passed, threshold, advisory)`. |
| `lambda_gate_batch(candidates, weights=None, threshold=0.5)` | Score many candidate vectors `(..., N, k)` in one call; returns the advisory pass mask. |
| `selfcheck()` | Empirical A1–A4 axiom checks + adversarial falsification search + version. NOT a uniqueness proof. |
| `is_monotone / is_homogeneous / is_egyptian_exact / is_bounded_by_max` | The four carried axioms as real runtime checks. |
| `yuyay_weights()`, `YUYAY_AXES`, `YUYAY_FLOORS` | Canonical 13-axis Yuyay preset (advisory). |
| layers: `LambdaGate`, `LambdaAggregate` | Pure `nn.Module` for the Kernel Hub layer-mapping mechanism. |

## Carried axioms (verifiable, not a proof)

- **A1 IsMonotone** — Λ is non-decreasing in each axis.
- **A2 IsHomogeneous (deg 1)** — Λ(t·x) = t·Λ(x).
- **A3 IsEgyptianExact** — Λ(c,…,c) = c.
- **A4 IsBounded** — Λ(x) ≤ maxᵢ xᵢ.

`selfcheck()` verifies these empirically on sampled inputs and runs a random falsification search. A clean run is **evidence, not proof** — Λ-uniqueness is Conjecture 1 (open).

## Provenance

Backed by the Lean 4 formalization [szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean) (749 declarations / 14 axioms / 163 tracked sorries), DOI [10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308). Λ uniqueness = Conjecture 1 (open).

## Honesty

- Pure-Python universal kernel — a correctness reference, not a CUDA speed record. No fabricated benchmarks (50 passing tests).
- Λ is advisory; never "proven trust."
- Prior art honestly attributed: the weighted geometric mean as a less-compensatory composite indicator is established practice (UN HDI 2010, OECD Composite Indicators Handbook 2008); the veto/cut-off idea is ELECTRE. The 13-axis conjunctive form is SZL's own yuyay_v3 gate.

## Compatibility

Python 3.9+, `torch>=2.5`, standard library + torch only.

## License

Apache-2.0. Copyright 2026 SZL Holdings.

---

## SZL Kernels Suite

Part of the [`szl-kernels`](https://huggingface.co/SZLHOLDINGS/szl-kernels) governed-kernel suite — the hub links every member, and each member links back to the hub so no leaf is orphaned:

| Kernel | Lane |
|---|---|
| [`szl-kernels`](https://huggingface.co/SZLHOLDINGS/szl-kernels) | **hub** — unified suite, cross-kernel `UnifiedReceiptChain` |
| [`szl-governed-norm`](https://huggingface.co/SZLHOLDINGS/szl-governed-norm) | RMSNorm/LayerNorm + SHA3-256 receipts |
| **`szl-lambda-gate`** (this repo) | **advisory Λ gate (Conjecture 1, OPEN)** |
| [`governed-inference-meter`](https://huggingface.co/SZLHOLDINGS/governed-inference-meter) | MEASURED-joule energy accounting (NVML) |
| [`szl-govsign`](https://huggingface.co/SZLHOLDINGS/szl-govsign) | signed governance attestation (DSSE / in-toto) |
| [`szl-blocked`](https://huggingface.co/SZLHOLDINGS/szl-blocked) | honest-BLOCKED state + EU AI Act Annex IV DRAFT |
| [`szl-provctl`](https://huggingface.co/SZLHOLDINGS/szl-provctl) | provenance-DAG verify + in-toto/SLSA interop |

**Live Spaces:** [a11oy](https://huggingface.co/spaces/SZLHOLDINGS/a11oy) · [hatun-mcp](https://huggingface.co/spaces/SZLHOLDINGS/hatun-mcp).

**Related — Governed Kernels collection:** [Governed Kernels — verifiable AI building blocks](https://huggingface.co/collections/SZLHOLDINGS/governed-kernels-verifiable-ai-building-blocks-6a41d3936cfce4fba83ce378) groups the whole family in one page. **Live console:** [a11oy](https://szlholdings-a11oy.hf.space) · [a-11-oy.com](https://a-11-oy.com) · [llm-router](https://szlholdings-llm-router-live.hf.space) · [receipt verifier](https://szlholdings-governed-receipt-verifier.static.hf.space) · [receipt spec (hub)](https://github.com/szl-holdings/governed-receipt-spec).


---

<sub><b>SZL Holdings</b> · Λ governance aggregator · advisory, not proven trust · <a href="https://a-11-oy.com">a-11-oy.com</a> · <a href="https://github.com/szl-holdings">github.com/szl-holdings</a> · <a href="https://huggingface.co/SZLHOLDINGS">huggingface.co/SZLHOLDINGS</a></sub>

---

[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.19944926.svg)](https://doi.org/10.5281/zenodo.19944926)

## Citation


**Cite this.** Part of the SZL Holdings *Ouroboros Thesis* (Governed Post-Determinism).  
Concept DOI (always-latest): [10.5281/zenodo.19944926](https://doi.org/10.5281/zenodo.19944926).  
Author: Stephen P. Lutar Jr. · [ORCID 0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173) · License CC-BY-4.0.  
Full DOI-pinned lineage (v1→v26) + the 8 papers: [szl-papers PAPERS_INDEX](https://github.com/szl-holdings/szl-papers/blob/main/PAPERS_INDEX.md).  
No artifact-specific DOI is minted for this model; the concept DOI above covers the program.

Honesty (Doctrine v11): Λ unconditional uniqueness is **Conjecture 1** (machine-checked FALSE as stated) — never a theorem; conditional uniqueness is **Theorem U** (axiom-free). Locked-proven formulas = **exactly 8** {F1,F4,F7,F11,F12,F18,F19,F22}; ~185 experimental theorems are a separate CI-green tier; Khipu BFT safety = Conjecture 2. Trust never 100%.

```bibtex
@misc{lutar_szl_ouroboros,
  author    = {Lutar, Stephen P., Jr.},
  title     = {SZL Holdings --- The Ouroboros Thesis (Governed Post-Determinism)},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.19944926},
  url       = {https://doi.org/10.5281/zenodo.19944926},
  note      = {Concept DOI --- always resolves to the latest version. ORCID 0009-0001-0110-4173. CC-BY-4.0.}
}
```

*Signed-off-by: Stephen Lutar <stephenlutar2@gmail.com>*

## Files in this repo

| Path | What it is |
|---|---|
| `build/torch-universal/szl_lambda_gate/__init__.py` | public API — `lambda_aggregate`, `lambda_gate`, `selfcheck()` |
| `build/torch-universal/szl_lambda_gate/_lambda.py` | the weighted-geometric-mean aggregator + A1–A4 empirical checks |
| `build/torch-universal/szl_lambda_gate/layers.py` | `nn.Module` wrapper |
| `build.toml` · `metadata.json` | Kernel Hub build/metadata manifests |
| `LICENSE` · `SECURITY.md` | Apache-2.0 · security policy |

---

<p align="center">
  <a href="https://huggingface.co/SZLHOLDINGS">SZL Holdings</a> ·
  <a href="https://a-11-oy.com">a-11-oy.com</a> ·
  <a href="https://huggingface.co/SZLHOLDINGS/szl-kernels">szl-kernels</a>
</p>

<p align="center"><sub>SLSA: L1 honest · L2 attested · L3 roadmap. Λ = Conjecture 1. Trust ceiling 0.97.</sub></p>